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Electromagnetic Fields in Biological Systems
electric fields at the two different pulse durations to ensure that a constant total energy
is maintained (Schoenbach et al. 2009). The difference arises from dielectric effects,
and in the ultrafast pulsing context, it is associated with the finite times required for
the reorientation of the dipoles within the system. For example, water (a polar material that surrounds the cell membrane) has a dielectric relaxation time of about 8 ps
(Buchner, Barthel, and Stauber 1999). This time is roughly the duration taken to displace the bonded charges within the molecular structures (e.g., polar water or the lipidic
cell membranes) by an external electric field. Similarly, there are other relaxation values that would be associated with the displacement of lipidic molecules within membranes. As a result, any applied electrical disturbance that occurs on timescales much
greater than ∼1 ns (as is the case for most conventional stimulations) will effectively see
conditions prevailing at near steady state. These include “quasistatic” dielectric constants and well-established screening layers adjacent to the membrane comprising of
charges and counterions. However, in the case of electric pulses that are shorter (e.g.,
in the subnanosecond regime), there will not be sufficient time for charge accumulation or the complete reorientation of the dipoles within either the aqueous medium or
the membrane hydrocarbons. Consequently, the effective dielectric constants seen by
the driving electric field, as well as the ratio of these parameters at the interfaces, will
be different. In short, by using ultrafast pulsing, it becomes technologically possible
to effectively select electrical parameters of the biosystem, different from the steadystate values. Biophenomena can then be driven under a distinctive and abnormal set of
parameters.
Several comprehensive and critical reviews of the dielectric properties of tissues and
biological materials have been given (Foster and Schwan 1989). The central idea is to
measure and evaluate the permittivities and conductivities of biotissues (and surrounding aqueous media). Using the notion of Fourier transforms and signal decomposition,
time-dependent quantities (such as charge kinetics and dipole movements) can most
conveniently be expressed in the frequency domain for linear responses. In the simplest
model, the polarization D of a sample/tissue will relax toward a steady state as a firstorder process with a relaxation time τ as follows:
D(t) = D ∞ + [D(0) − D ∞ ] [1 – e –t/τ ]
(2.16)
where D ∞ is the “instantaneous” response that might arise if the system could respond
extremely fast with no lag time, while D(0) is the steady-state response after a long time.
The time constant τ given in Equation 2.16 depends on the process and can be as short
as subnanoseconds (e.g., reorientation of short molecules) to seconds (for counterion
redistributions). As a result, the dielectric constant (a measure of electrical screening) is
then expressed in the frequency domain as follows:
ε = ε ∞ + [ε(0) − ε ∞ ]/[1 + jωτ] − jσ 0 /(ω ε 0 )
(2.17)
where ε ∞ and ε(0) denote the dielectric constants at very large and near-zero frequencies,
respectively, and σ 0 is the static conductivity. Thus experimentally, the principal objective is to obtain data on the ε(0), ε ∞ , and σ 0 parameters.